Colouring simplicial complexes via the Lechuga-Murillo's model

Abstract

L. Lechuga and A. Murillo showed that a non-oriented, simple, connected, finite graph $G$ is $k$-colourable if and only if a certain pure Sullivan algebra associated to $G$ and $k$ is not elliptic. In this paper, we extend this result to simplicial complexes by means of several notions of colourings of these objects.

arXiv comment7 pages. The article has been rewritten following the comments of a referee, to whom I am grateful for their feedback which helped greatly improve the presentation of this work. To appear in Appl. Algebra Engrg. Comm. Comput